The Annals of Probability
- Ann. Probab.
- Volume 6, Number 5 (1978), 705-730.
Sufficient Statistics and Extreme Points
A convex set $M$ is called a simplex if there exists a subset $M_e$ of $M$ such that every $P \in M$ is the barycentre of one and only one probability measure $\mu$ concentrated on $M_e$. Elements of $M_e$ are called extreme points of $M$. To prove that a set of functions or measures is a simplex, usually the Choquet theorem on extreme points of convex sets in linear topological spaces is cited. We prove a simpler theorem which is more convenient for many applications. Instead of topological considerations, this theorem makes use of the concept of sufficient statistics.
Ann. Probab., Volume 6, Number 5 (1978), 705-730.
First available in Project Euclid: 19 April 2007
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Dynkin, E. B. Sufficient Statistics and Extreme Points. Ann. Probab. 6 (1978), no. 5, 705--730. doi:10.1214/aop/1176995424. https://projecteuclid.org/euclid.aop/1176995424